IITJEE questions

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2007 IITJEE PAPER - 1

A )

B )

54 μ C

C )

27 μ C

D )

81 μ C

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A )	A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.

B )	A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.

C )	No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders

D )	No potential difference appears between the two cylinders when same charge density is given to both the cylinders

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A )	E (²³⁶₉₂ U) > E (¹³⁷₅₃ I) + E (⁹⁷₃₉ Y) + 2 E (n)

B )	E (²³⁶₉₂ U) < E (¹³⁷₅₃ I) + E (⁹⁷₃₉ Y) + 2 E (n)

C )	E (²³⁶₉₂ U) < E (¹⁴⁰₅₆ Ba) + E (⁹⁴₃₆ Kr) + 2 E (n)

D )	E (²³⁶₉₂ U) = E (¹⁴⁰₅₆ Ba) + E (⁹⁴₃₆ Kr) + 2 E (n)

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A )

x < f

B )	f < x < 2f

C )

x = 2f

D )

x > 2f

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A )

802 nm

B )

823 nm

C )

1882 nm

D )

1648 nm

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A )

3 Ω

B )

4 Ω

C )

5 Ω

D )

6 Ω

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A )	only a reflected ray and no refracted ray

B )	only a refracted ray and no reflected ray

C )	a reflected ray and a refracted ray and the angle between them would be less than 180^° - 2 θ

D )	a reflected ray and a refracted ray and the angle between them would be greater than 180^° - 2 θ

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8) Two particles of mass 'm' each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each ease is at a distance a from the centre P (as shown in the figure). Now, the mid-point d the string is pulled vertically upwards with a small but constant force F. As a result, the parrt1cles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

A )

B )

C )

D )

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A )	negative and distributed uniformly over the surface of the sphere

B )	negative and appears only at the point on the sphere closest to the point charge

C )	negative and distributed non-uniformly over the entire surface of the sphere

D )

zero

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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12) STATEMENT-1
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 300 with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.
because
STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )

P₀

B )

P₀

C )

P₀	+	Mg
2		π R²

D )

P₀	-	Mg
2		π R²

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A )

B )

C )

D )

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16) A fixed thermally conducting cylinder has a radius R and height L₀. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P₀.

The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies

A )	ρg(L₀ - H)² + P₀(L₀ - H) + L₀P₀ = 0

B )	ρg(L₀ - H)² - P₀(L₀ - H) - L₀P₀ = 0

C )	ρg(L₀ - H)² + P₀(L₀ - H) - L₀P₀ = 0

D )	ρg(L₀ - H)² - P₀(L₀ - H) + L₀P₀ = 0

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A )

B )

1/2

C )

D )

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18) Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity 2 ω using the entire potential energy of a spring compressed by a distance x₁. Disc B is imparted an angular velocity ω by a spring having the same spring constant and compressed by a distance x₁. Both the discs rotate in the clockwise direction.

When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

A )

2 I ω

3 t

B )

9 I ω

2 t

C )

9 I ω

4 t

D )

3 I ω

2 t

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A )

I ω²

B )

I ω²

C )

I ω²

D )

I ω²

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20) Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 X 4 matrix given in the ORS.

Column I

Column II

(A)
GM_eM_s
G → universal gravitational constant, M_e → mass of the earth,
M_s → mass of the sun,

(p)
(volt) (coulomb) (metre)

(B)

3 R T

R → universal gas constant, T → absolute temperature, M → molar mass

(q)
(kilogram) (metre)³ (second)^-2

(C)

F²

q²B²

F → force, q → charge, B → magnetic field

(r)
(meter)² (second)^-2

(D)

G M_e

R_e

G → universal gravitational constant, M_e → mass of the earth, R_e → radius of the earth

(s)
(farad) (volt)² (kg)^-1

Answer:
A → (p)&(q) , B → (r) & (s), C → (r) & (s), D → (r) & (s)

A )

B )

C )

D )

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21) Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) Transition between two atomic energy levels	(p) Characteristic X - rays
(B) Electron emission from a material	(q) Photoelectric effect
(C) Mosley's law	(r) Hydrogen spectrum
(D) Change of photon energy into kinetic energy of electrons	(s) β - decay

Answer:
A → (p) & (r), B → (q) & (s), C → (p), D → (q)

A )

B )

C )

D )

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22) Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) A charged capacitor is connected to the ends of the wire	(p) A constant current flows through the wire
(B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion	(q) Thermal energy is generated in the wire
(C) The wire is placed in a constant electric field that has a direction along the length of the wire.	(r) A constant potential difference develops between the ends of the wire
(D) A battery of constant emf is connected to the ends of the wire	(s) Charges of constant magnitude appear at the ends of the wire

Answer:
A → (q), B → (r) & (s), C → (r) & (s), D → (p), (q) & (r)

A )

B )

C )

D )

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A )

B )

C )

D )

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A )

B )

C )

D )

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A )

0.5

B )

C )

D )

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A )

Na₂O

B )

O₃

C )

Na₂O

D )

KO₂

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A )

B )

C )

D )

100

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A )

NO^-

B )

NO⁺

C )

CN^-

D )

N₂

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A )

B )

C )

D )

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A )	electrolytic reduction

B )	roasting followed by reduction with carbon

C )	roasting followed by reduction with another metal

D )	roasting followed by self-reduction

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A )	alcoholic KOH

B )	alcoholic KOH followed by NaNH₂

C )	aqueous KOH followed by NaNH₂

D )

Zn/CH₃OH

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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36) Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 X 10²³) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.

A 4.0 molar aqueous solution of NaCl is prepared and 500 mL of this solution is electrolysed. This leads to the evolution of chlorine gas at one of the electrodes (atomic mass: Na = 23, Hg = 200; 1 Faraday=96500 coulombs)

The total number of moles of chlorine gas evolved is

A )

0.5

B )

1.0

C )

2.0

D )

3.0

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37) Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 X 10²³) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.

If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is

A )

200

B )

225

C )

400

D )

446

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38) Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 X 10²³) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.

The total charge (coulombs) required for complete electrolysis is

A )

24125

B )

48250

C )

96500

D )

193000

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39) The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers +2, +4 and +6. XeF₄ reacts violently with water to give XeO₃. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.

Argon is used in arc welding because of its

A )	low reactivity with metal

B )	ability to lower the melting point of metal

C )	flammability

D )	high calorific value

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40) The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

The structure of XeO₃ is

A )

linear

B )

planar

C )

pyramidal

D )

T-shaped

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41) The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

XeF₄ and XeF₆ are expected to be

A )

oxidizing

B )

reducing

C )	unreactive

D )	strongly basic

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42) Match the complexes in Column-I with their properties listed in Column-II. Indicate your answer by darkening the appropriate bubbles of the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) [Co(NH₃)₄(H₂O)₂]Cl₂	(p) geometrical isomers
(B) [Pt(NH₃)₂Cl₂]	(q) paramagnetic
(C) [Co(H₂O)₅Cl]Cl	(r) diamagnetic
(D) [Ni(H₂O)₆]Cl₂	(s) metal ion with +2 oxidation state

Answer:
A → (p, q, s), B → (p, r, s), C → (q, s), D → (q, s)

A )

B )

C )

D )

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43) Match gases under specified conditions listed in Column-I with their properties/laws in Column-II. Indicate your answer by darkening the appropriate bubsbles of the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) hydrogen gas (P = 200 atm, T = 273K)	(p) compressibility factor ≠ 1
(B) hydrogen gas (P ~ 0, T = 273K)	(q) attractive forces are dominant
(C) CO₂ (P = 1 atm, T = 273K)	(r) PV = nRT
(D) real gas with very large molar volume	(s) P(V - nb) = nRT

Answer:
A → (p, s), B → (r), C → (p, q), D → (p, s)

A )

B )

C )

D )

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44) Match the chemical substances in Column-I with type of polymers/type of bonds in Column-II. Indicate your answer by darkening the appropriate bubbles of the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) cellulose	(p) natural polymer
(B) nylon-6, 6	(q) synthetic polymer
(C) protein	(r) amide linkage
(D) sucrose	(s) glycoside linkage

Answer:
A → (p, s), B → (q, r), C → (p, r), D → (s)

A )

B )

C )

D )

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A )	x²cosec²θ - y²sec²θ = 1

B )	x²sec²θ - y²cosec²θ = 1

C )	x²sin²θ - y²cos²θ = 1

D )	x²cos²θ - y²sin²θ = 1

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A )	on the left of x = c

B )	on the right of x = c

C )	at no point

D )	at all points

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A )	3 e^iπ/4 + 4 i

B )	(3 - 4 i)e^iπ/4

C )	(4 + 3 i)e^iπ/4

D )	(3 + 4 i)e^iπ/4

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A )

1	+	2x²
3x	+	3

B )

-	1	+	4x²
	3x		3

C )

-	1	+	2
	x		x²

D )

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A )

zero

B )

one

C )

two

D )

four

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A )

2	(p - q) (2q - p)
9

B )

2	(q - p) (2p - q)
9

C )

2	(q - 2p) (2q - p)
9

D )

2	(2p - q) (2q - p)
9

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A )

zero

B )

one

C )

two

D )

three

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A )

1/2

B )

1/3

C )

2/5

D )

1/5

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A )

8	f(2)
π

B )

2	f(2)
π

C )

2	f (	1	)
π		2

D )

4 f(2)

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )	Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

B )	Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

C )	Statement-1 is True, Statement-2 is False.

D )	Statement-1 is False, Statement-2 is True.

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A )

1 :

B )

1 : 2

C )

1 : 4

D )

1 : 8

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A )

B )

C )

D )

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A )

B )

C )

8/3

D )

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A )

1	n(n + 1) (3n² - n + 1)
12

B )

1	n(n + 1) (3n² + n + 1)
12

C )

1	n (2n² - n + 1)
2

D )

1	n (2n³ - 2n + 3)
3

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A )	an odd number

B )	an even number

C )	a prime number

D )	a composite number

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A )	Q₁, Q₂, Q₃, ...are in A.P. with common difference 5

B )	Q₁, Q₂, Q₃, ...are in A.P. with common difference 6

C )	Q₁, Q₂, Q₃, ...are in A.P. with common difference 11

D )	Q₁ = Q₂ = Q₃ = ...

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64) Consider the following linear equations

ax + by + cz = 0
bx + cy + az = 0
cx + ay + bz = 0
Match the conditions / expressions in Column I with statements in Column II and indicate your answers by darkening the appropriate bubbles in 4 X 4 matrix given in the ORS.

Column I Column II

(A)
a + b + c ≠ 0 and a² + b² + c² = ab + bc + ca (p)
the equations represent planes meeting only at a single point.

(B)
a + b + c = 0 and a² + b² + c² ≠ ab + bc + ca (q)
the equations represent the line x = y = z.

(C)
a + b + c ≠ 0 and a² + b² + c² ≠ ab + bc + ca (r)
the equations represent identical planes.

(B)
a + b + c = 0 and a² + b² + c² = ab + bc + ca (s)
the equations represent the whole of the three dimensional space.

Answer:
A → (r) , B → (q), C → (p), D → (s)

A )

B )

C )

D )

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65) Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 X 4 matrix given in the ORS.

Column I

Column II

(A)

(p)

1	log (	2	)
2		3

(B)

(q)

2 log (	2	)
	3

(C)

(r)

(D)

(s)

Answer:
A → (s) , B → (s), C → (p), D → (r)

A )

B )

C )

D )

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66) In the following [X] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties Column II and indicate your answer by darkening the appropriate bubbles in the 4 X 4 matrix given in the ORS.

Column I	Column II
(A) x \|x\|	(p) continuous in (-1, 1)
(B)	(q) differentiable in (-1, 1)
(C) x + [x]	(r) strictly increasing in (-1, 1)
(D) \|x - 1\| + \|x + 1\|	(s) not differentiable at least at one point in (-1, 1)

Answer:
A → (p,q,r) , B → (p,s), C → (r,s), D → (p,q)

A )

B )

C )

D )

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Final result and score
Q No	Ans	Correct Ans	Score	Q No	Ans	Correct Ans	Score
1	-		0	2	-		0
3	-		0	4	-		0
5	-		0	6	-		0
7	-		0	8	-		0
9	-		0	10	-		0
11	-		0	12	-		0
13	-		0	14	-		0
15	-		0	16	-		0
17	-		0	18	-		0
19	-		0	20	-		0
21	-		0	22	-		0
23	-		0	24	-		0
25	-		0	26	-		0
27	-		0	28	-		0
29	-		0	30	-		0
31	-		0	32	-		0
33	-		0	34	-		0
35	-		0	36	-		0
37	-		0	38	-		0
39	-		0	40	-		0
41	-		0	42	-		0
43	-		0	44	-		0
45	-		0	46	-		0
47	-		0	48	-		0
49	-		0	50	-		0
51	-		0	52	-		0
53	-		0	54	-		0
55	-		0	56	-		0
57	-		0	58	-		0
59	-		0	60	-		0
61	-		0	62	-		0
63	-		0	64	-		0
65	-		0	66	-		0
Final score : 0

Answer sheet
Q No	Ans	For review	Q No	Ans	For review
1			2
3			4
5			6
7			8
9			10
11			12
13			14
15			16
17			18
19			20
21			22
23			24
25			26
27			28
29			30
31			32
33			34
35			36
37			38
39			40
41			42
43			44
45			46
47			48
49			50
51			52
53			54
55			56
57			58
59			60
61			62
63			64
65			66